Observed $1/f$ Noises

When a process is assumed to be random and treated as such, the accuracy and scale of its power spectrum depends on the accuracy and stability of the equipment and the method of observation of the signal. Keshner[20] lists many observed fluctuations which behave like $1/f$ noise. These phenomena range from the voltage or currents of vacuum tubes, diodes, and transistors; the resistance of carbon microphones and semiconductors; the frequency of quartz crystal oscillators; the voltage across nerve membranes, to average seasonal temperature, annual amount of rainfall, rate of traffic flow, economic data; and finally, as Voss and Clarke claim, in pitch and loudness of music.

One would imagine that if these phenomena were observed for a very long period of time or with very high precision, one would find regions in the power spectrum which either act as white noise or as deterministic processes. Currently science has a difficult time understanding the $1/f$ noise since it is neither a deterministic periodic (or quasi-periodic) nor a random signal. Some experimenters have measured the $1/f$ noise in MOSFET's down to ${10}^{-6.3}$ Hz, or 1 cycle in 3 weeks. Other experimenters have computed the weather data using geological techniques to ${10}^{-10}$ Hz, or 1 cycle in 300 years. Yet still in neither of these cases was any change observed in the power spectrum. Keshner points to two cases (the resistance of fluctuations of thin-films, and of tin film at the temperature of the superconducting transition and in the voltage fluctuations across nerve membranes) where changes were observed.